[BUG]: Objects created using __new__ are not registered for casting

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What version (or hash if on master) of pybind11 are you using?

3.0.1

Problem description

When a pybind-based object or a subclass of one is created using new, it is not added to the registry of pybind objects for casting. If the object has methods than require casting to return the correct type information for its actual subtype, then this silently breaks those methods.

This is somewhat related to issue #1693, as using the listed workaround is how I found this problem.

Reproducible example code

Suppose we have:

#include <pybind11/pybind11.h>

using namespace py = pybind11;

struct Num {
    double n;
    Num(double n) : n(n) {}
    
    inline Num Mult2() { return Num(2 * n) }
}

PYBIND11_MODULE(this_example, m) {
    py::class_<Num> pyNum(m, "Num");

    pyNum
    .def(py::init([]() { return Num(0); }))
    .def("mult2", [](const Num *self) {
        py::object selfObj = py::cast(self);
        PyTypeObject *const ty = Py_TYPE(selfObj.ptr());
        auto newObj = py::reinterpret_steal<py::object>(ty->tp_new(ty, py::list().ptr(), py::dict().ptr()));
        *newObj.cast<Num*>() = self->Mult2();
        return newObj;
    })
    .def_readwrite("n", &Num::n);
}



from this_example import Num

class MoreNum(Num):
    def mult4(self):
        ret = self.__class__.__new__(self.__class__)
        ret.n = self.n * self.n
        return ret

# Works, but returned object is not registered.
MoreNum().mult2()
MoreNum().mult4()
MoreNum().mult2().mult4()

# mult4 is not implemented on Num
MoreNum().mult2().mult2().mult4()

Is this a regression? Put the last known working version here if it is.

Not a regression

Start by building the reproducible C++ pybind11 example and running the shown Python calls involving Num, MoreNum, new, mult2, and mult4. Trace how py::class_ objects created through new enter the pybind11 object registry; done means these objects are registered and chained calls preserve the actual subtype behavior.